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Author Topic: Spring Garden I  (Read 519 times)
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Pauldelbrot
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Posts: 2592



pderbyshire2
« on: March 27, 2012, 07:58:35 AM »

Spring Garden I



http://www.fractalforums.com/index.php?action=gallery;sa=view;id=10831

The Supernova fractal, which is the one capable of producing Herman rings, produces seahorses everywhere if the alpha parameter is set to 0.51803398 and b is set to zero while the c-plane is visualized. There are two fixed attractors, zero and infinity. Purple points go to various other, parameter-dependent attractors; these cluster into Mandelbrot shapes arrayed along lines. The remaining points are fought over by the two fixed attractors, and they weave a very complicated boundary between them in the dynamic plane, features of which get reproduced in the parameter plane.

In this image, the parameters for which the selected critical point escapes are colored with a multiwave gradient that starts out pink, then shades into reds, oranges, greens, and eventually purples and other colors. Parameters where the c.p. goes to zero get a cyan-to-blue-to-... multiwave.

A notable feature of Supernova is that the seahorse "eyes" are transformed into lakes with inverted seahorse features around them; the lakes' points are captured by the opposite basin to the rest of the seahorse. The lake shores are among the best minibrot hunting grounds, as we shall eventually see.
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